Arguably, the concept of "individual" is incoherent even with ordinary humans, for at least two reasons.

First, one could argue that human brain doesn't operate as a single agent in any meaningful sense, but instead consists of a whole bunch of different agents struggling to gain control of external behavior -- and what we perceive as our stream of consciousness is mostly just delusional confabulation giving rise to the fiction of a unified mind thinking and making decisions. (The topic was touched upon in this LW post and the subsequent discussion.)

Second, it's questionable whether the concept of personal identity across time is anything more than an arbitrary subjective preference. You believe that a certain entity that is expected to exist tomorrow can be identified as your future self, so you assign it a special value. From the evolutionary perspective, it's clear why humans have this value, and the concept is more or less coherent assuming the traditional biological constraints on human life, but it completely breaks down once this assumption is relaxed (as discussed in this recent thread). Therefore, one could argue that the idea of an "individual" existing through time has no objective basis to begin with, and the decision to identify entities that exist in different instants of time as the same "individual" can't be other than a subjective whim.

I haven't read and thought about these problems enough to form a definite opinion yet, but it seems to me that if we're really willing to go for a no-holds-barred reductionist approach, they should both be considered very seriously. Trouble is, their implications don't sound very pleasant.